Tag Archives: mathematics

Bill Gates dismisses it – this belief that children can construct their own understanding of mathematics. Many educators disagree.

John Van de Walle’s student-centred approach? Marilyn Burns’ insight into how children learn math? The rationale in the WNCP curriculum? The beliefs of the BCAMT? Gates would dismiss them all.

More importantly to me, he would dismiss the successes that Surrey teachers and students experience when teachers let go and give students a chance to do the math. “Letting go” does not mean students are left to discover the Pythagorean Theorem on their own. The role of the constructivist teacher is to get students mentally ready to work on a task, listen, provide hints, and facilitate discussion.

Instead, Gates supports the Khan Academy and the flipped classroom model. In this model, students watch a video at home so that they can get one-on-one homework help at school. Sometimes, flipping proponents claim that this model frees the teacher up to have students do real problem solving. With all the press that the flipped classroom is getting, there is surprisingly little anecdotal evidence of this actually happening.

Gates, Khan, and others have missed the point. Problem solving isn’t something you do after you have learned a concept. That’s practice. Students should solve problems not to apply but to learn new mathematics. The flipped classroom model removes teachers from the most important part of teaching – the introduction of new concepts.

Suppose the proverbial teacher across the hall doesn’t buy in to “all that constructivist stuff” and is considering flipping his or her classroom. Here are three questions that I would ask:

1. Does teaching = telling? (See how I made that a math question?)

I understand if the general public views teaching as simply delivering content, it’s probably what they experienced as learners. Teaching, like real estate, is one of those careers that everyone thinks they can do. I guess I expect my fellow educators to know better. I thought we no longer viewed children as empty vessels to be filled with knowledge. I thought we were moving away from seeing curriculum as topics to “get through.” I thought we were moving towards an emphasis on the mathematical processes. Earning badges online seems like a giant step backwards to me.

2. When you are explaining a new concept, is the interaction between you and your students important?

I have a confession to make. For most of my career, I have used a teacher-centred approach. Still, even in this traditional lecture format, students were given opportunities to ask me clarifying questions or check their understanding with a neighbour. I was able to pick up on subtle non-verbal cues and adapt my lesson on the fly. Throughout my career, all of my attempts to improve my teaching have me moving towards a more student-centred approach, not searching for a more efficient way to deliver a lecture.

3. How does replacing a one-size-fits-all lecture with a one-size-fits-all video meet the needs of all of your students?

Flipping proponents exclaim, “Kids can pause and rewind videos! They can watch them over and over again!” Yeah. But it’s still the same video. This reminds me of the time I was lost in Naples. I asked a local for directions to the train station. He patiently repeated, in Italian, the directions to me several times. I was still lost. Last year, Dr. Marian Small spoke with almost 100 secondary math teachers from Surrey about differentiating instruction. Surrey teachers are beginning to use her two core strategies: open questions and parallel tasks. The ultimate goal of differentiation is to meet the varied learning needs of all students, not to have students complete a series of videos at their own pace.

My final objection to the flipped model is that it is being held up as revolutionary. Assigning a video lecture for homework, and then working on 1 to 49 odd in class instead of watching a lecture in class, and then working on 1 to 49 odd for homework should not be considered a revolution in math education. (If this flip did result in higher scores on standardized tests, does it matter?) We know that real change is difficult. Flipping a classroom isn’t – all that is needed is a tablet PC.

I would like to redefine what flipping a classroom means. My idea of a flipped classroom would be one in which students, not the teacher, are doing the math. Instead of teacher-created videos, the tools of my flipped classroom would be chart paper, felt markers, and sticky notes.

Technology will also play a role. In Surrey, secondary science/math teacher Blair Miller uses video, in the style of Dan Meyer, to ask engaging questions. His students use Vernier Video Physics, an iPad app, to analyze functions. His students interact with dynamic applets that he has created using GeoGebra.

These are effective uses of technology. This is a revolution that I can get behind.

about.me

Dreaming big. Making it happen. I live an adventure. I choose it to be an adventure.I am an educator. My love is leadership. I am fascinated by good ideas, system change, innovation and scaling up transformation.I believe when people find the intersection of their purpose and passion they can live out their calling. I help others flourish—so they can do the best work of their lives. I build human capacity.I believe in trust, transparency and truth as pivotal to organizational health. These cornerstones must be evident at the top in order to permeate our organizations.I love working with others, some days. I love being intensely alone, some days. I like to hide in a book. Run long with the wind. Walk in the wild. And do absolutely nothing.I crave outrageous family vacations. I make memories for my four boys: ages 10, 13, 17, & 20. And I am committed to making the world a better place for them.I want to remember to be kind. Yes, there is simplicity in kindness. It truly is a measure of the heart.Joyfully obeying the call.